In this paper, we study an integrated production and outbound distribution scheduling model with one manufacturer and one customer. The manufacturer has to process a set of jobs on a single machine and deliver them in batches to the customer. Each job has a release date and a delivery deadline. The objective of the problem is to issue a feasible integrated production and distribution schedule minimizing the transportation cost subject to the delivery deadline constraints. We consider three problems with different ways how a job can be produced and delivered: non-splittable production and delivery (NSP-NSD) problem, splittable production and non-splittable delivery (SP-NSD) problem and splittable production and delivery (SP-SD) problem. We provide a polynomial-time algorithm that solves two special cases of SP-NSD and SP-SD problems. Solving these problems allows us to compute a lower bound for the NP-hard problem NSP-NSD, which we use in a branch and bound (B&B) algorithm to solve problem NSP-NSD. The computational results show that the B&B algorithm outperforms a MILP formulation of the problem implemented on a commercial solver. keywords: single machine scheduling production and delivery release dates deadlines transportation costs branch and bound.